Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit

TL;DR

This paper demonstrates a continuous-variable geometric phase in a superconducting circuit and leverages it to implement efficient, multi-qubit controlled-phase gates, advancing quantum computation methods with noise resilience.

Contribution

It introduces a novel geometric phase-based quantum gate protocol in superconducting circuits enabling one-step multi-qubit gates, reducing complexity compared to traditional methods.

Findings

Successfully observed a continuous-variable geometric phase.

Implemented n-qubit controlled-phase gates up to n=4.

Verified high efficiency and noise resilience of the geometric approach.

Abstract

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multiqubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of $n$-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with $n$. Following this approach, we realize these gates with $n$ up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.